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the diagram shows graphs of y=1/2x+2 and 2y+2x=12. Use the diagram to solve the simultaneous equations

2 Answers

6 votes

Answer:


\mathsf {(2.66, 3.33)}

Step-by-step explanation:


\textsf {Given :}


\mathsf {1) y = (1)/(2)x + 2}


\mathsf {2) 2y + 2x = 12} \implies \mathsf {y + x = 6} \implies \mathsf {y = -x + 6}


\mathsf{Solving :}


\textsf {Equating the values of y from both equations :}


\implies \mathsf {(1)/(2)x + 2 = -x + 6}


\implies \mathsf {(3)/(2)x = 4}


\implies \mathsf {3x = 8}


\implies \mathsf {x = (8)/(3) \implies {x = 2.66...}}


\textsf {Finding y :}


\implies \mathsf {y = -(8)/(3) + 6}


\implies \mathsf {y = (18 - 8)/(3)}


\implies \mathsf {y = (10)/(3)} \implies \mathsf {y = 3.33...}


\textsf {Graph of equations is attached below.}

the diagram shows graphs of y=1/2x+2 and 2y+2x=12. Use the diagram to solve the simultaneous-example-1
User Ivan Milosavljevic
by
8.1k points
5 votes

Answer: (2.67, 3.33)

Step-by-step explanation:

For the function y = 1/2x + 2

  • y-intercept = (0, 2)
  • x-intercept = (-4, 0)


\hrulefill

For the function 2y + 2x = 12

  • y-intercept = (0, 6)
  • x-intercept = (6, 0)

Draw lines through these coordinates to produce a straight linear graph.

Then see, where they intersect each other. Intersection point : (2.67, 3.33)

the diagram shows graphs of y=1/2x+2 and 2y+2x=12. Use the diagram to solve the simultaneous-example-1
User Laurea
by
7.6k points

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